Abstract
According to one of the more popular endurantist packages on the market, a package I will call multilocational endurantism, enduring objects are exactly located at multiple instantaneous regions of spacetime. However, for all we know, the world might turn out to be spatiotemporally gunky and spatiotemporal gunk (with some natural assumptions) entails that this package is false. The goal of this paper is to sketch a view which retains the spirit of multilocational endurantism while also recognizing the possibility of certain types of objects which endure through gunk.
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Notes
See Sider (2001), pp. 63–68.
What I call the mereological, measure-theoretic, and multilocational variants of endurantism correspond roughly to what Effingham (2012) calls populationism, dimensionalism, and occupationalism, respectively.
With the multilocational endurantist, this paper will assume that spacetime substantivalism is true, i.e., that spacetime regions exist and are not reducible to spatiotemporal relations among material objects. This paper will also ignore complications from relativity theory.
The term ‘gunk’ was coined by Lewis (1991), who used it to refer to infinitely divisible atomless objects. There are other ways a world might not contain spacetime points. For instance, a world could be chunky, i.e., composed of minimal, extended spacetime tiles (perhaps no smaller than a Planck length). This view will be briefly discussed in passing, but our central concern in this paper is gunky spacetime.
In particular, he writes “In the first place, such states [i.e., states that correspond to point values for continuous observables] cannot exist in the standard separable Hilbert space formulation. They can be introduced, but only at the expense of a prima facie less natural formulation of quantum particle mechanics. Moreover, exact value states for one observable imply undefined expectation values for many other observables. Indeed, it seems hard to make sense of the probabilities of the results of measurements of perfectly ordinary observables when one starts out, for example, in a position eigenstate” (p. 1457).
Strictly speaking, the thesis that spacetime is gunky does not entail the thesis that there are no instantaneous regions of spacetime. Arntzenius and Hawthorne (2005) make a similar point about spatial gunk: consider a spatial point P which is gunky but where each of its infinitely many proper parts are co-located with P. Similarly, consider a model with one instantaneous region of spacetime R which is gunky but where each of R’s proper subregions are co-located with R. But for the purposes of this paper, let’s ignore exotic models with co-located regions of spacetime. When I say gunk threatens multilocational endurantism, what I really mean is that the thesis that spacetime is gunky together with the thesis that there are no instantaneous regions entails the conclusion that multilocational endurantism is false.
Multilocational endurantism is defended/endorsed in van Inwagen (1990a, b), Gilmore (2007), Bittner et al. (2004) and Sattig (2006); it is discussed/explored in Hawthorne (2006, 2008), (2009) and (2014a), Donnelly (2010), Kleinschmidt (2011), Effingham (2012), Eagle (2016a, b); it is explored in the context of relativity theory in Balashov (2010, 2011), and Gilmore (2006); it is objected to or rejected in Gilmore (2006), Calosi (2010), Balashov (2011), Hofweber and Velleman (2011), and Costa (Forthcoming); and some replies and rejoinders appear in Gibson and Pooley (2006), Eagle (2010a, b), Gilmore (2010), and Rychter (2011).
This gloss is taken from Gilmore (2007), though note that Gilmore calls this relation “exact occupation.” See p. 179, n. 7. I take “exact location” to mean what Varzi (2007) means by “exact location,” what Gilmore (2006) and Hudson (2001) mean by “exactly occupies,” what Donnelly (2010) means by “is exactly located at,” what Sattig (2006) means by “occupies,” and what Hawthorne (2008) means by “is wholly located at.”
As in Effingham (2012).
Thanks to Jeff Russell for this way of putting it.
Apparently, Pythagoras’ disciples credited him with the power of bi-location. See Kenny (1998), p. 2.
The formulation of multilocational endurantism I provide is a little more precise than what is typically offered in the literature. But it’s meant to rule out some cases which I would think multilocational endurantists would not want to classify as cases of endurance. I’ll mention three. First, it rules out an enduring object o which is only exactly located at two spatially disjoint and yet simultaneous regions R and S. One might think that this should, however, count as a case of endurance and think of this case as an exotic case of time-travel. I’m inclined to think that since the object only ever exists at one “instant,” it is more natural to think of this case as a case of instantaneous space-travel (rather than genuine time-travel), and thus not as a case of persistence (after all, a familiar intuitive slogan is: something persists iff it exists at more than one time). But if one disagrees, then one is free to drop the requirement that a persisting object needs a non-instantaneous path (with some fix to prevent a mono-located instantaneous object counting as an enduring object; also note that the third problem below would also need to be dealt with). Thanks to a referee for bringing up the idea of time-travel in this scenario. Second, it rules out an enduring object o which endures through some region R but then is also exactly located at a temporally extended region \(R^\prime \) which is disjoint from R: o would endure through R but would not endure simpliciter. Third, there are models where (1) there are instantaneous regions and (2) all regions are gunky. In this sort of model, every instantaneous region has an instantaneous region as a proper part, i.e., we have a plenitude of coincident regions. (The analogous model demonstrating the consistency of gunky space and the existence of spatial points is discussed in Arntzenius and Hawthorne 2005). Suppose an object o was exactly located at one and only one “gunky instantaneous region.” The requirement that a persisting object’s path be non-instantaneous ensures us that an object which is multiply located at such a region is not in fact an enduring object.
I should note two further complications. First, suppose an object is exactly located at only two instantaneous regions of spacetime. Should this count as a case of endurance? I’m not sure what the multilocational endurantist would want to say about this case so I remain neutral in the formulation of the view, but if she wanted to not characterize this case as a case of endurance, perhaps she could simply place a further constraint on the definition of an object’s path by requiring that it be continuous. Second, time-travel complicates things. Suppose that a brick is instantaneously created with the width of ten inches and endures for one minute. It then travels back through time in such a way to be adjacent to itself for another minute, and then is destroyed. The brick’s path will be a four-dimensional region which is both one minute long and 20 inches wide, but there will be no maximal instantaneous 20 inch part of the path at which the brick is exactly located, and thus the brick doesn’t endure simpliciter. While I should admit that the purpose of this paper is not to deal with every possible sort of exotica, to deal with this problem, we might say that an object o endures simpliciter iff for every maximal part \(P^\prime \) of its path P, o is located at a subregion (proper or improper) of \(P^\prime \). However, I want to note in passing that these sorts of exotic time-travel cases won’t be problematic for the novel view I’ll propose near the end of the paper − the enduring time-traveling brick will correctly be classified as an enduring object.
Assuming, of course, that at least some objects persist.
Other versions of endurantism seem to handle spatiotemporal gunk just fine. First, consider the mereological version of endurantism developed in Parsons (2000, 2007) (it’s worth noting that not all endurantists find this version of persistence to be a clear version of endurantism, since one might be worried that on this view, it’s not obvious that objects are wholly present at every time at which they exist). The view is called terdurantism by Miller (2009), transdurantism by Daniels (2014), and pardurantism by Effingham (2012). On this view, enduring objects are four dimensional temporally extended simples. For such an object o, the exact location of o is some four-dimensional region of spacetime. But if spacetime is gunky, then o’s exact location is gunky, and o endures through time by being wholly present at a (albeit gunky) four-dimensional region of spacetime. A very interesting and similar version of endurantism (albeit a supersubstantivalist version) is explored in Nolan (2014). On a second endurantist package, sketched in Hawthorne (2008) and recently developed in Hofweber and Velleman (2011), say that an object is wholly located at a region of spacetime just in case it is intrinsic to how things are at that region that that very object exists at that region. And to say that a material object is wholly located at each time at which it exists amounts to saying, as Hawthorne notes, that “God could recognize me as present at any given time that I exist just by considering the world at that time, as it is in itself” (p. 276). If the world is in fact temporally gunky, then this package suggests that an object o enduring through time, say \(t_0-t_n\), amounts to God being able to look at any interval d in \(t_0-t_n\) and see that o is present, just based on the intrinsic nature of d itself.
It’s important to note that we now cannot take ‘maximal part’ as defined in the previous section. Here is one way of defining it in the present context. Supposing there is a temporal partial ordering on gunky regions: a part p of a path P is maximal iff it is the intersection of P with that region S which is the fusion of all regions s such that none of s is strictly earlier than any of p, and none of s is strictly later than any of p. Thanks to an anonymous referee for this definition.
And for the endurantist who thinks that plenitudinous endurers are possible, the standard responses to the problem of temporary intrinsics are available. She could, for instance, relativize properties to spatiotemporal regions and thus say that Plenitudinous Pythagoras is F at \(R_1\) but not \(R_2\). Or she could accept some form of adverbialism and say that Plenitudinous Pythagoras is F \(R_1\)-ly though not \(R_2\)-ly. Or she could tense the copula: Plenitudinous Pythagoras is-at-\(R_1\) F though is-not-at-\(R_2\) F. Of course, enduring objects can gain and lose parts, so it follows that such objects have different sizes and shapes at different regions.
Plenitudinous endurers are inconsistent with a principle of mereological harmony (on mereological harmony, see Varzi 2007; Uzquiano 2011; Saucedo 2011; Leonard 2016): x is a proper part of y iff x’s exact location is a proper part of y’s exact location. Since Plenitudinous Pythagoras is exactly located at both \(R_1\) and P, and since \(R_1\) is a proper part of P, it follows from our principle of harmony that Plenitudinous Pythagoras is a proper part of himself, which is absurd. Some might take this as a reason to think that plenitudinous endurers are impossible. However, the second type of object which endures through spatiotemporal gunk (sketched in the subsequent section) does not violate these sorts of harmony principles.
Are there objects which are not plenitudinous endurers, but close? And if so, should they count as cases of endurance? Here are two types of examples (one which counts given (Multilocation*), and one which might or might not). First, suppose an object \(o_1\) is exactly located at some spacetime region R and also every closed subregion of R (though not the open ones). Or similarly, suppose an object \(o_2\) is exactly located at some spacetime region R and also every subregion of R with a rational temporal length (but not an irrational temporal length). Though there will be tons of gaps (for instance, o won’t be exactly located at maximal parts of its path with irrational temporal lengths), and though \(o_1\) and \(o_2\) are not strictly speaking plenitudinous endurers, they nonetheless endure simpliciter, since they are exactly located at maximal disjoint parts of every maximal non-instantaneous part of their paths. A second case was suggested by an anonymous referee. Say that a region is homogenous iff it is qualitatively uniform. Now say that a region is homo-maximal iff it is homogeneous and is not a part of any homogeneous region. Now consider an object that is exactly located at every maximal homo-maximal part of its path. With this model, we can look at the pattern of qualitative variation over an object’s path, find the slices that correspond to qualitative change, and then locate the object at just those regions which are bounded by qualitative changes but are qualitatively homogenous internally. Given the above definition, so long as these objects are located at maximal disjoint parts of every maximal non-instantaneous part of their paths, they count as enduring objects. However, this is not guaranteed: consider a little model where an object is red for a year and then green for a year (and that’s it). This object will be located at a region corresponding to the first year, though no maximal proper subregions of that region, and thus by (Multilocation*), will not count as a case of endurance.
A natural idea would be to treat thin endurers just like plenitudinous endurers, with respect to the problem of temporary intrinsics. Relationalism, adverbialism, and copula-tensing seem to all be live options for how to model a thin endurer which changes its properties over time.
And each of which is discussed in Section 3 of Parsons (2007).
See Parsons (2007), f.n. 4.
Parsons (2007) notes, however, that an extended simple hovering over the sill of my window would be neither entirely in my office nor entirely in the street, though it would be wholly in my office and wholly in the street. See p. 212.
Thanks to both an anonymous referee and Dean Zimmerman for pushing me on this point.
As pointed out by an anonymous referee, note we can avoid this problem if we treat all objects as mereologically simple (and if we deny DAUP and related principles), and if we reduce mereological variation to qualitative variation. Then, Pythagoras would be wholly located at R-North and wholly located at R-South, and instantiate the qualitative property ‘being 10-fingered’ at R-North, and the qualitative property ‘being 9-fingered’ at R-South. This, however, is not likely a view many endurantists will go for and thus I suggest that we really need a primitive containment relation for the formulation of endurantism.
Elsewhere, Eagle (2010a) says that o is contained in R iff all of o’s parts are located at subregions of R. This too is distinct from my containment primitive, since according to my primitive, an object can be contained in a region and not be exactly located anywhere.
If the reader remains skeptical about the meaning of the primitive, the central claim of the paper can be read as a conditional: if one understands the primitive, then the paper explores what can be done with it. Moreover, it would be interesting to construct a logic of containment and explore exactly how containment relates to other notions of location. However, once we allow for the possibility of multilocation, a number of similar location relations become quite difficult to define. I’ll leave developing a logic of containment for an independent project.
In the first section of the paper, I noted that sometimes ‘path’ is taken as a primitive and sometimes it is defined as the fusion of an object’s exact locations. But given that we are taking seriously the possibility of states of affairs where objects lack exact locations, we cannot define it in terms of exact location. So instead, I’ll officially take it as a primitive.
At least in the context of gunky space, though not discrete space.
Of course, not every set of converging sub-intervals converges on a point. The best way of mathematically characterizing Whiteheadian points (and thus Whiteheadian times) is not important for our purposes, but see Roeper (1997) for some details.
Though there are a number of ways of trying to make this option work, it nonetheless comes with undesirable results. I’ll first mention some ways of trying to make this option work, and then mention a problem. First, though multilocational endurantists maintain that the fundamental feature of endurantism concerns location, they typically reject the existence of material objects which have proper temporal parts. And thus, on mereological grounds, the defender of the current option could deny that objects with proper temporal parts endure simpliciter (by insisting that no objects with proper temporal parts actually exist). Second, one might be interested in positing certain bridge principles governing the relationship between weak location and exact location. Here is a principle which would be very natural for the multilocational endurantist to accept:
(Weak-Exactness): If an object o is weakly located at every member of a Whiteheadian time t, and there exists an instantaneous region of spacetime R such that t converges to R, then o is exactly located at R.
This principle, though a bit brute, suggests that if the world turns out to contain instantaneous regions of spacetime, mono-located temporally extended simples are metaphysically impossible. However, a related worry remains. Temporally extended simples located in temporal gunk remain classified as enduring objects on the present approach (since (Weak-Exactness) doesn’t entail that these types of objects are metaphysically impossible) and this, I take it, is an undesirable classification for the multilocational endurantist.
For helpful comments and discussion, I’d like to thank Claudio Calosi, Cruz Davis, Maegan Fairchild, Cody Gilmore, Chris Healow, Shieva Kleinschmidt, Kristie Miller, Josh Parsons, Oliver Pooley, Ted Sider, Jim Van Cleve, Achille Varzi, Jennifer Wang, Dean Zimmerman, a number of very helpful anonymous referees, and audiences at the University of Oxford, USC, UC Berkeley, Virginia Tech, the 2016 Pacific APA, and the Metaphysics of Space, Time, and Spacetime conference in Alghero, Italy. Special thanks to John Hawthorne, Jeff Russell, and Gabriel Uzquiano for feedback on a number of drafts.
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Leonard, M. Enduring Through Gunk. Erkenn 83, 753–771 (2018). https://doi.org/10.1007/s10670-017-9912-4
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DOI: https://doi.org/10.1007/s10670-017-9912-4